Cafe Am Heumarkt is a traditional yet eccentric Viennese coffee house that I find fascinating. It serves straightforward Viennese cuisine with no tourist extras – schnitzel, pancakes, coffee and beer. Open 9am-11pm Monday to Friday, it’s rarely busy, word of mouth being its only advertisement. There’s no sign above its door: to find it I had to search for the intriguingly incognito exterior of 15 Am Heumarkt, behind the Hotel Intercontinental near the Stadtpark.

The dark wooden bar and high ceiling supported by thick stone pillars are typical of Vienna’s coffee houses, but it’s a far cry from the city’s usual chandeliered establishments. The cavernous space is unadorned, sparsely furnished, and echoes like an old school hall. In the centre of the expansive parquet floor sit two ancient display fridges, which are indeed filled with Viennese tarts and cakes, but produce an insistent, noisy buzzing, like beleaguered washing machines.

Marble tabletops and 1950s-style red leather booths give you a sense of stepping back in time. Elderly men mutter over games of backgammon or read newspapers near the always-empty billiard tables. Instead of smart livery, the waiters wear lab coats over string vests – a genuinely incongruous and perplexing uniform that only accentuates their dour expressions.

Friendliness takes the form of dry – extremely dry – humour and a stern proprietary concern for patrons. Otherwise, the staff hide in the kitchen and – the locals joke – ensure the cafe is closed on weekends and holidays for fear of attracting custom.

Though the food is tasty and reasonably priced, it’s not what lures me here repeatedly. It’s the curiously charming ambience of anti-cafe: the anomalous phenomenon that is Cafe Am Heumarkt.

• Holly Müller’s first novel, My Own Dear Brother, is published this month by Bloomsbury Circus (£14.99). To order a copy for £11.99 including UK p&p visit the Guardian bookshop or call on 0330 333 6846